Question

find the number of digits in the smallest number which is made up of digits 1 and 0 only and is divisible by 225.

Answer 1

Let the average speed of passenger train be x km/h.

Average speed of express train = (x + 11) km/h

It is given that the time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance.

⇒ 132 × 11 = x(x + 11)

⇒ x2 + 11x - 1452 = 0

⇒ x2 + 44x -33x -1452 = 0

⇒ x(x + 44) -33(x + 44) = 0

⇒ (x + 44)(x - 33) = 0

⇒ x = - 44, 33

Speed cannot be negative.

Therefore, the speed of the passenger train will be 33 km/h and thus, the speed of the express train will be 33 + 11 = 44 km/h.